Related papers: Quantitative Languages Defined by Functional Autom…
Describing systems in terms of choices and their resulting costs and rewards offers the promise of freeing algorithm designers and programmers from specifying how those choices should be made; in implementations, the choices can be realized…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
We study a model of one-way quantum automaton where only measurement operations are allowed ($\mon$). We give an algebraic characterization of $\lmo(\Sigma)$, showing that the syntactic monoids of the languages in $\lmo(\Sigma)$ are exactly…
Formal grammars are extensively used in Computer Science and related fields to study the rules which govern production of a language. The use of these grammars can be extended beyond mere language production. One possibility is to view…
We introduce the notion of multipass automata as a generalization of pushdown automata and study the classes of languages accepted by such machines. The class of languages accepted by deterministic multipass automata is exactly the Boolean…
Affine automata provide a finite-state computational model that preserves the linear-algebraic structure of quantum computation while operating entirely over the reals. Recent work has shown that affine automata can far surpass classical…
Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…
Using a novel rewriting problem, we show that several natural decision problems about finite automata are undecidable (i.e., recursively unsolvable). In contrast, we also prove three related problems are decidable. We apply one result to…
This paper studies the complexity of operations on finite automata and the complexity of their decision problems when the alphabet is unary. Let $n$ denote the maximum of the number of states of the input finite automata considered in the…
We study decidability of verification problems for timed automata extended with unbounded discrete data structures. More detailed, we extend timed automata with a pushdown stack. In this way, we obtain a strong model that may for instance…
In a recent paper we have described an optical implementation of a measure-once one-way quantum finite automaton recognizing a well-known family of unary periodic languages, accepting words not in the language with a given error…
This work addresses the problem of computing measures of recognisable sets of infinite trees. An algorithm is provided to compute the probability measure of a tree language recognisable by a weak alternating automaton, or equivalently…
We explore a natural class of semigroups that have word problem decidable by finite state automata. Among the main results are invariance of this property under change of generators, invariance under basic algebraic constructions and…
Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…
We study three notions of directability of fuzzy automata akin to the D1-, D2- and D3-directability of nondeterministic automata. Thus an input word $w$ of a fuzzy automaton is D1-directing if a fixed single state is reachable by $w$ from…
The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is…
In this paper we regard languages and their acceptors -- such as deterministic or weighted automata, transducers, or monoids -- as functors from input categories that specify the type of the languages and of the machines to categories that…
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
Large language models (LLMs) often benefit from verbalized reasoning at inference time, but it remains unclear which aspects of task difficulty these extra reasoning tokens address. To investigate this question, we formalize a framework…
Automata learning is a technique that has successfully been applied in verification, with the automaton type varying depending on the application domain. Adaptations of automata learning algorithms for increasingly complex types of automata…